factor26 wrote:If s is the product of the integers from 100 to 200 inclusive, and if t is the product of the integers from 100 to 201 inclusive, what is 1/s + 1/t in terms of t?
A. (201)^2/t
B. {(202)(201)}/t
C. 201/t
D. 202/t
E. {(202)(201)}/t^2
The correct answer is D ... any insight on how to solve this would be greatly appreciated ... Thanks!!
s =
100*101*102.....198*199*200
t =
100*101*102.....198*199*200*201
t =
s*201
Notice that s and t share the factors in red.
The only difference between s and t is that t has one additional factor: 201.
In other words, t =
s*201.
We can plug in ANY VALUES for s and t that satisfy the condition that t = 201s.
Let s = 2.
Then t = 201s = 201*2 = 402.
1/s + 1/t = 1/2 + 1/402 = 402/804 + 2/804 = 404/804 = 101/201. This is our target.
Now we plug t=402 into the answers to see which yields our target of 101/201.
Only answer choice
D works:
202/t = 202/402 = 101/201.
The correct answer is
D.
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